Moyuru Ochiai

Crossover behavior of systems associated with extended-defect N-component systems in cubic anisotropic crystals

Extended-defect N-component systems in cubic anisotropic crystals have fixed points of the Gaussian [G], Ising [PI], isotropic N-component [PN] and cubic anisotropic N-component [PcN] systems as regular (pure) systems, and those of the Ising [DI], isotropic N-component [DN], cubic anisotropic XY [DcXY] and cubic anisotropic N-component [DcN] systems as extended-defect systems. Crossover behavior near these typical fixed point systems is studied by means of a renormalization-group (RG) approach and characteristic curve (CC) method. Crossover exponents of the systems and their behavior are calculated and illustrated to linear order in ϵ (≡ − d; d = dimension of space) and ≈ϵ (≡ϵ + ϵd; ϵd = dimension of space occupied by extended defects (impurities)).

Self-similarity law of particle size distribution and energy law in size reduction of solids

The concept of fractal dimension and scaling is used to determine the particle size distribution for ground powder and a generalized energy law for size reduction of solids. Based on the theory of stochastic processes, a master equation for the size distribution under a sieve is introduced. For the case that the functional forms of the transition probabilities are given, the solution is analutically obtained. Introducing a scaling concept and a characteristic size constant which measures the particle size distribution of the ground product, we present a power law for the distribution function. We, furthermore, present a generalized fractal energy law which has an intimate relation to the size distribution through a fractal specific surface area.

On the critical dynamics of extended-impurity systems in cubic anisotropic crystals

Critical dynamics is studied for N-component spin systems in cubic anisotropic crystals in the presence of extended impurities, namely ed-dimensionally connected impurities distributed randomly in d∼ (≡ d − ed) dimensions (d: dimensionality of the medium; d ≡ 4 - e). As extended impurities make the systems coordinate-anisotropic, new results are expected in the critical dynamics. By means of a field-theoretic renormalization-group (RG) approach, critical regions and dynamic critical exponents are evaluated, to the lowest order in a double e, ed expansion, for models corresponding to model A, model B and model C, proposed by Hohenberg and Halperin.

Static and dynamic properties of XY systems with extended defects in cubic anisotropic crystallines

Static and dynamic critical behavior ofXY systems in cubic anisotropic crystallines, with extended defects (or quenched nonmagnetic impurities) strongly correlated alongɛd-dimensional space and randomly distributed ind − ɛd dimensions, were studied. These extended defects make the systems coordinate anisotropic, resulting in unique critical behavior due to competition between the cubic anisotropy and the coordinate anisotropy. The systems were analyzed by anɛ1/2 (ɛ≡4 − d) type of expansion with double expansion parameters based on a renormalization-group (RG) approach. Critical exponents were calculated near the second-order phase transition point and the behavior of the first-order transition was evaluated near the tricritical point.

Adaptive–intelligent control by neural‐net systems

Adaptive–intelligent control by neural‐net systems is discussed. Actual adaptive–intelligent control is realized in a general system through the following two hierarchical steps: (1) choosing a hierarchical coordinate system (associated with the environment of the system) and constructing the hierarchical evaluation functions (specifying its control states) and (2) finding a set of the most appropriate hierarchical values for the control parameters (giving the minimum value to the evaluation function). Step 1 establishes “intelligently self‐controllable (thinking) algorithms” with human‐like intelligence for various events (concepts). Step 2 studies the intelligently self‐controllable (thinking) algorithms for finding the most appropriate state. Adaptive–intelligent control by neural‐net systems is realized by integrating both intelligently self‐controllable (thinking) algorithms on the neural‐net systems. Here step 2 is mainly discussed in the neural‐net systems of Boltzmann type machines using the method of stochastic dynamics.

Critical behavior of N-component spin systems with random impurities in cubic-anisotropy crystalline material

Static and dynamic critical behavior of N-component spin systems with cubic anisotropy and with quenched random impurities are studied in the limit ed→0+ of the impurity system whose impurities are strongly correlated in ed dimensions while they are randomly distributed in the remaining d − ed dimensions. By means of the renormalization-group approach, the stability of the fixed points, the flow of the interactions and the critical exponents are evaluated up to two-loop order. The behavior of the first order phase transition to appear is also studied.

Thermoanalytical characterization of powder samples I. Wet pretreated samples

Routine wet pretreatment of a powder sample causes a drastic change in the thermoanalytical results. The pretreatment may alter the crystallographic or molecular structure, but more distinguished change occurs in the powder characteristics. Thus, consistent thermoanalytical results can be obtained by subjecting the powder sample to wet pretreatment for classification.

Dipole decay function and dielectric loss curve of polymers in dilute solution

A dielectric relaxation of vinyl‐type polymers in dilute solution is theoretically studied with the aid of the dipole decay function (the macroscopic time correlation function). An extension of Anderson’s model for the time‐dependent statistics of the Ising chain is used for the purpose. An evaluating method for the macroscopic decay function of chains with finite length is given, and results of numerical calculations under various conditions are presented.

Application of neural network algorithm to CAD of magnetic systems

Abstract Magnetic systems comprise some of the most useful devices in the world, e.g. magnets for magnetic resonance images (MRI), nuclear magnetic resonance (NMR), and linear motors and accelerators. Generally, their constituent magnetic-elements have a strongly nonlinear and finite magnetic permeability, and their magnetic materials are hard and difficult to cut, in addition to being expensive. For determination of the best shape of magnetic systems and the best selection of magnetic materials, it is useful to investigate CAD (computer-aided design) systems based on electromagnetic theory using the material relations (magnetic flux density-magnetization (B-M) curves). Our aims are to construct general CAD systems appropriate for macro- to nano-machines, but in the present paper we focus our attention on the shape design of a simple permanent magnet as an example. Our CAD system is constructed with two parts to determine (1) the self-consistent distribution of magnetization under a certain shape and (2) the best shape which gives the minimum volume. We show that in both cases a neural network algorithm (which we developed) can play a powerful role.

REGRESSION LAW OF FLUCTUATIONS AND SELF-SIMILARITY LAW AT A CRITICAL POINT IN DIFFUSION-REACTION PROCESSES

Regression law of fluctuations and self-similarity law in chemical systems far from equilibrium are studied. In the case of a system far from equilibrium including a bifurcation point, the conventional perturbation treatment useful for such small fluctuations as described by Gaussian approximation, becomes irrelevant. An asymptotic method of analysis of large fluctuations in chemical systems at a critical point is developed. A master equation describing the dynamics of a chemical system, which is written by newly defined generating functions, is basic. Fluctuations at a critical point give rise to a macroscopic effect and behave nonlinearly. It is shown that even at such a bifurcation point the hypothesis called the regression law of fluctuations is still valid.